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Simplifying ln(1 + -4b) = ln(4b + 9) (1 * ln + -4b * ln) = ln(4b + 9) Reorder the terms: (-4bln + 1ln) = ln(4b + 9) (-4bln + 1ln) = ln(4b + 9) Reorder the terms: -4bln + 1ln = ln(9 + 4b) -4bln + 1ln = (9 * ln + 4b * ln) Reorder the terms: -4bln + 1ln = (4bln + 9ln) -4bln + 1ln = (4bln + 9ln) Solving -4bln + 1ln = 4bln + 9ln Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4bln' to each side of the equation. -4bln + -4bln + 1ln = 4bln + -4bln + 9ln Combine like terms: -4bln + -4bln = -8bln -8bln + 1ln = 4bln + -4bln + 9ln Combine like terms: 4bln + -4bln = 0 -8bln + 1ln = 0 + 9ln -8bln + 1ln = 9ln Add '-1ln' to each side of the equation. -8bln + 1ln + -1ln = 9ln + -1ln Combine like terms: 1ln + -1ln = 0 -8bln + 0 = 9ln + -1ln -8bln = 9ln + -1ln Combine like terms: 9ln + -1ln = 8ln -8bln = 8ln Divide each side by '-8ln'. b = -1 Simplifying b = -1
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